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Despite the convention, "cotton kills," in the desert those same properties (slow drying, water retention) are useful for keeping you cool by slowing down the near instant evaporation experienced at such high heat and low humidity. Your goal is to make that moisture work as long for you as possible.

Since "water is 24.5 times more conductive than air," (according the an answer found here) water will conduct your body heat away from you more rapidly, making you cooler. Synthetics aid in wicking that heat-sapping moisture away and making it disappear -- which is what you want when trying to stay warm, but NOT what you want when trying to stay cool.

I also soak my shirt in water whenever available, and am always astounded by how fast it dries (even cotton).

So, to summarize: Long sleeve light colored thin fabric cotton is leagues better than any synthetic.

(Originally posted as part of this answer then copied here and expanded.)

@manoftheson About the same in my experience - often the linen is a looser weave allowing for more breatheability but less water retention. There's a reason its popular in tropic areas like India.
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LBellJan 12 '13 at 1:30